Topological quantum computation is based on the possibility of the realization of some TQFTs in Nature as topological phases of quantum matter. Theoretically, we would like to classify topological phases of matter, and experimentally, find non-abelian objects in Nature. We will discussion some progress for a general audience.

Experiments and observations over the last decade and a half have persuaded cosmologists that (as yet undetected) dark energy is by far the main component of the energy budget of the universe. I review a few simple dark energy models and compare their predictions to observational data, to derive dark energy model-parameter constraints and to test consistency of different data sets. I conclude with a list of open cosmological questions.

After the completion of the Planck satellite, the next most important experiments in cosmology will be about mapping the Large Scale Structures of the Universe. In order to continue to make progress in our understanding of the early universe, it is essential to develop a precise understanding of this system. The Effective Filed Theory of Large Scale Structures provides a novel framework to analytically compute the clustering of the Large Scale Structures in the weakly non-linear regime in a consistent and reliable way.

In describing condensed matter, some well established paradigms have allowed much progress to be made in understanding and using materials. But in the last 15 - 20 years, new materials, such as heavy fermions, high temperature superconductors, and now charge density wave-supporting materials, have been shown to require new paradigms in describing them. While much progress has been achieved in that time, we still do not have a widely accepted theoretical description of the nature of their electronic excitations.

The QCD axion is a curious Dark Matter candidate, having a mass like the neutrino, but behaving as Cold Dark Matter. I will review how this occurs, and discuss the interesting question of whether WIMPs could be distinguished from axions with Large Scale Structure data.

I'll discuss some recent results, motivated by the black-hole firewall paradox and the AdS/CFT correspondence, about the quantum circuit complexity of preparing certain entangled states and implementing certain unitary transformations.

Entropy comes up all over physics and mathematics in many different guises. However, as one tries to understand its conceptual meaning, entropy often evades the question by shifting into a different shape. Here, I will try to capture the beast by surrounding it from all sides. Assistance by the audience will increase the chance of success.

Recent developments reveal a deep connection between entanglement entropy and the emergence of space time and gravity. In anti-de Sitter space gravity appears to be derived from the first law of thermodynamics for entanglement entropy, which in the large radius limit obeys an area law. Based on insights from string theory, we propose a generalisation of these results to flat space and de Sitter space. In the latter case, the vacuum entanglement entropy has an additional contribution that scales like the volume of the bulk space time.

The known basic building blocks of matter, the quarks and leptons, come in three generations or flavors.

The masses and interactions of the different flavors show a very hierarchical structure and the origin of these hierarchies remains an unsolved mystery of particle physics. The same hierarchies lead to a very high sensitivity of flavor changing processes to new undiscovered particles even outside the reach of direct searches at particle colliders.